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Measuring Electricity
Electricity Measurement
Electricity makes our lives easier, but it can seem like a mysterious force. Measuring electricity is confusing because we cannot see it. We are familiar with terms such as watt, volt, and amp, but we may not have a clear understanding of these terms. We buy a 60-watt light bulb, a tool that needs 120 volts, or a vacuum cleaner that uses 8.8 amps, and we don’t think about what those units mean. Using the flow of water as an analogy can make electricity easier to understand. The flow of electrons in a circuit is similar to water flowing through a hose. If you could look into a hose at a given point, you would see a certain amount of water passing that point each second.
The amount of water depends on how much pressure is being applied—how hard the water is being pushed. It also depends on the diameter of the hose. The harder the pressure and the larger the diameter of the hose, the more water passes each second. The flow of electrons through a wire depends on the electrical pressure pushing the electrons and on the cross-sectional area of the wire.
Voltage
The pressure that pushes electrons in a circuit is called voltage (V). Using the water analogy, if a tank of water were suspended one meter above the ground with a 1-cm diameter pipe coming out of the bottom, the water pressure would be similar to the force of a shower. If the same water tank were suspended 10 meters above the ground, the force of the water would be much greater, possibly enough to hurt you. Voltage is a measure of the pressure applied to electrons to make them move. It is a measure of the strength of the current in a circuit and is measured in volts (V). Just as the 10-meter high tank applies greater pressure than the 1-meter high tank, a 10-volt power supply (such as a battery) would apply greater pressure than a 1-volt power supply. AA batteries are 1.5 volts; they apply a small amount of voltage or pressure for lighting small flashlight bulbs. A car usually has a 12-volt battery—it applies more voltage to push current through circuits to operate the radio or defroster. The standard voltage of wall outlets is 120 volts—a dangerous amount of voltage. An electric clothes dryer is usually wired at 240 volts—a very dangerous voltage.
Current
The flow of electrons can be compared to the flow of water. The water current is the number of molecules flowing past a fixed point; electric current (I) is the number of electrons flowing past a fixed point. Electric current is defined as electrons flowing between
Voltage
Water Tank
Water Tank
1 m 10 m
Current
Water Tank Water Tank
1 cm diameter pipe 10 cm diameter pipe
two points having a difference in voltage. Current is measured in amperes or amps (A). One ampere is 6.25 X 1018 electrons per second passing through a circuit. With water, as the diameter of the pipe increases, so does the amount of water that can flow through it. With electricity, conducting wires take the place of the pipe. As the cross-sectional area of the wire increases, so does the amount of electric current (number of electrons) that can flow through it.
Measuring Electricity
Resistance
Resistance (R) is a property that slows the flow of electrons. Using the water analogy, resistance is anything that slows water flow, a smaller pipe or fins on the inside of a pipe. In electrical terms, the resistance of a conducting wire depends on the metal the wire is made of and its diameter. Copper, aluminum, and silver—metals used in conducting wires—have different resistance. Resistance is measured in units called ohms (Ω). There are devices called resistors, with set resistances, that can be placed in circuits to reduce or control the current flow. Any device placed in a circuit to do work is called a load. The light bulb in a flashlight is a load. A television plugged into a wall outlet is also a load. Every load has resistance.
Ohm’s Law
George Ohm, a German physicist, discovered that in many materials, especially metals, the current that flows through a material is proportional to the voltage. In the substances he tested, he found that if he doubled the voltage, the current also doubled. If he reduced the voltage by half, the current dropped by half. The resistance of the material remained the same. This relationship is called Ohm’s Law, and can be written in three simple formulas. If you know any two of the measurements, you can calculate the third, using the formulas to the right.
Electric Power
Power (P) is a measure of the rate of doing work or the rate at which energy is converted. Electric power is the rate at which electricity is produced or consumed. Using the water analogy, electric power is the combination of the water pressure (voltage) and the rate of flow (current) that results in the ability to do work. A large pipe carries more water (current) than a small pipe. Water at a height of 10 meters has much greater force (voltage) than at a height of one meter. The power of water flowing through a 1-centimeter pipe from a height of one meter is much less than water through a 10-centimeter pipe from 10 meters. Electric power is defined as the amount of electric current flowing due to an applied voltage. It is the amount of electricity required to start or operate a load for one second. Electric power is measured in watts (W).
ELECTRIC POWER FORMULA
Power = voltage x current P= V x I or W = V x A
Resistance
Water Tank Water Tank
No Resistance Resistance
OHM’S LAW
Voltage = current x resistance V = I x R or V = A x Ω Current = voltage / resistance I = V / R or A = V / Ω Resistance = voltage / current R = V / I or Ω = V / A
Electric Power
Water Tank
10 cm pipe
Water Tank
1 m 1 cm pipe 10 m
Electrical Energy
Electrical energy introduces the concept of time to electric power. In the water analogy, it would be the amount of water falling through the pipe over a period of time, such as an hour. When we talk about using power over time, we are talking about using energy. Using our water example, we could look at how much work could be done by the water in the time that it takes for the tank to empty. The electrical energy that an appliance or device consumes can be determined only if you know how long (time) it consumes electric power at a specific rate (power). To find the amount of energy consumed, you multiply the rate of energy consumption (measured in watts) by the amount of time (measured in hours) that it is being consumed. Electrical energy is measured in watt-hours (Wh).
Energy (E) = Power (P) x Time (t)
E = P x t or E = W x h = Wh
Another way to think about power and energy is with an analogy to traveling. If a person travels in a car at a rate of 40 miles per hour (mph), to find the total distance traveled, you would multiply the rate of travel by the amount of time you traveled at that rate. If a car travels for 1 hour at 40 miles per hour, it would travel 40 miles.
Distance = 40 mph x 1 hour = 40 miles
If a car travels for 3 hours at 40 miles per hour, it would travel 120 miles.
Distance = 40 mph x 3 hours = 120 miles
The distance traveled represents the work done by the car. When we look at power, we are talking about the rate that electrical energy is being produced or consumed. Energy is analogous to the distance traveled or the work done by the car. A person wouldn’t say he took a 40-mile per hour trip because that is the rate. The person would say he took a 40-mile trip or a 120-mile trip. We would describe the trip in terms of distance traveled, not rate traveled. The distance represents the amount of work done. The same applies with electric power. You would not say you used 100 watts of light energy to read your book, because a watt represents the rate you use energy, not the total energy used. The amount of energy used would be calculated by multiplying the rate by the amount of time you read. If you read for five hours with a 100W bulb, for example, you would use the following formula:
Energy = Power x Time
E = P x t
Energy = 100 W x 5 hours = 500 Wh
One watt-hour is a very small amount of electrical energy. Usually, we measure electric power in larger units called kilowatt-hours (kWh) or 1,000 watt-hours (kilo = thousand). A kilowatt-hour is the unit that utilities use when billing most customers. The average cost of a kilowatt-hour of electricity for residential customers is about 13 cents.
To calculate the cost of reading with a 100-W bulb for 5 hours, you would change the watt-hours into kilowatt-hours, then multiply the kilowatt-hours used by the cost per kilowatt-hour, as shown below: 500 Wh x = 0.5 kWh 1 kW 1,000W
0.5 kWh x $0.13/kWh = $0.065
It would cost a little more than six cents to read for five hours using a 100-W bulb.
